Single-species Population Dynamics Research Articles

Effects of survival thresholds upon one-dimensional dynamics of single-species populations

A simple one-dimensional model of single-species populations is studied by means of computer simulations. Although the model has a rich spectrum of dynamics including chaotic behavior, the introduction of survival thresholds makes the chaotic region so small that it can be hardly observed. Stochastic fluctuations further reduce the chaotic region because they accidentally lead populations to extinction. The model thus naturally explains the observation that the majority of natural populations do not show chaotic behavior but a monotonic return to a stable equilibrium point following a disturbance.

Effects of survival thresholds upon one-dimensional dynamics of single-species populations

Effects of survival thresholds upon one-dimensional dynamics of single-species populations

From Physiology to Population Dynamics and Communities

Levels of organization provide one of the central themes around which biologists attempt to understand the living world. Mechanistic explanations for behaviour at one level tend to be couched in terms of behaviour of lower level systems; the hierarchy is familiar, running from cell biology and biochemistry, to physiology, individual behaviour, population dynamics, communities, and ultimately ecosystems and the biosphere. Generally the most useful explanations link adjacent steps in the hierarchy. Here, I explore a very small part of what physiology can tell us about populations and communities of animals, concentrating on drawing attention to promising lines for further research. Schoener (1986) and Kingsolver (1989) adopt a similar approach but cover very different aspects of the same general problem. My specific aim is to show how simple, tactical models of energy acquisition and use by individual animals generate understanding of both population dynamics and species' distributions. The principle concern of the paper is with the rules determining rates of energy assimilation, respiration and production by individual animals. In broad terms, the physiology of resource acquisition and use provides the scaling rules within which populations and communities must operate (Peters, 1983, 1986). This paper focuses upon metabolic rate, particularly maintenance metabolism and the partitioning of assimilated energy between metabolism and production. It then links these processes to single-species population dynamics, as well as to predator-prey and competitive interactions, and goes on to explore in a very tentative manner the size of species' geographic ranges, and questions of tropical and temperate species' diversity.

Periodic solutions of a nonlinear autonomous age-dependent model of single species population dynamics

Periodic solutions of a nonlinear autonomous age-dependent model of single species population dynamics

Boundary-layer model for the population dynamics of single species

We develop a new discrete-time model, called the boundary-layer model, to describe the dynamics of single species that have a capacity for fast growth at very low population densities. The model explicitly separates the dynamics of the population at very low densities (within the "boundary layer") and at high densities. The boundary-layer model provides a better fit than other models such as the logistic or the theta model to data from experimental populations of Drosophila willistoni and D. pseudoobscura.

Periodic Solutions of a Nonlinear Age-Dependent Model of Single Species Population Dynamics

A system of nonlinear differential and integral equations, derived in an earlier paper as a model of single species population dynamics, is studied under the general assumption that the birth rate decreases or the death rate increases as the total population increases. Lower and upper uniform asymptotic bounds are determined for solutions of the model, and sufficient conditions are determined for the existence of periodic solutions.

Populations and Simple Food Webs as Energy Filters. I. One Species Systems

Previous articleNext article No AccessPopulations and Simple Food Webs as Energy Filters. I. One Species SystemsS. P. HubbellS. P. Hubbell Search for more articles by this author PDFPDF PLUS Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinkedInRedditEmail SectionsMoreDetailsFiguresReferencesCited by The American Naturalist Volume 107, Number 953Jan. - Feb., 1973 Published for The American Society of Naturalists Article DOIhttps://doi.org/10.1086/282819 Views: 5Total views on this site Citations: 12Citations are reported from Crossref Copyright 1973 The University of Chicago.PDF download Crossref reports the following articles citing this article:David A. Vasseur Populations embedded in trophic communities respond differently to coloured environmental noise, Theoretical Population Biology 72, no.22 (Sep 2007): 186–196.https://doi.org/10.1016/j.tpb.2007.06.002Owen L. Petchey Environmental colour affects aspects of single–species population dynamics, Proceedings of the Royal Society of London. Series B: Biological Sciences 267, no.14451445 (Apr 2000): 747–754.https://doi.org/10.1098/rspb.2000.1066 Joel G. Kingsolver , and Ward B. Watt Thermoregulatory Strategies in Colias Butterflies: Thermal Stress and the Limits to Adaptation in Temporally Varying Environments, The American Naturalist 121, no.11 (Oct 2015): 32–55.https://doi.org/10.1086/284038Homer T. Hayslett Sources of Applications of Mathematics in Ecological and Environmental Subject Areas, Suitable for Classroom Use, (Jan 1983): 137–168.https://doi.org/10.1007/978-1-4612-5430-0_7Joel Kingsolver The effect of environmental uncertainty on morphological design and fluid balance in Sarracenia purpurea L., Oecologia 48, no.33 (Mar 1981): 364–370.https://doi.org/10.1007/BF00346496H.I. Freedman, Paul Waltman Mathematical analysis of some three-species food-chain models, Mathematical Biosciences 33, no.3-43-4 (Jan 1977): 257–276.https://doi.org/10.1016/0025-5564(77)90142-0PETER H. ASTOR, BERNARD C. PATTEN, GERALD N. ESTBERG The Sensitivity Substructure of Ecosystems, (Jan 1976): 389–429.https://doi.org/10.1016/B978-0-12-547204-3.50054-3 Jonathan Roughgarden A Simple Model for Population Dynamics in Stochastic Environments, The American Naturalist 109, no.970970 (Oct 2015): 713–736.https://doi.org/10.1086/283039Albert J. Ammerman Late pleistocene population dynamics: An alternative view, Human Ecology 3, no.44 (Oct 1975): 219–233.https://doi.org/10.1007/BF01531424BERNARD C. PATTEN, DAVID A. EGLOFF, THELMA H. RICHARDSON Total Ecosystem Model for a Cove in Lake Texoma, (Jan 1975): 205–421.https://doi.org/10.1016/B978-0-12-547203-6.50018-9 Jonathan Roughgarden Population Dynamics in a Spatially Varying Environment: How Population Size "Tracks" Spatial Variation in Carrying Capacity, The American Naturalist 108, no.963963 (Oct 2015): 649–664.https://doi.org/10.1086/282941 S. P. Hubbell Populations and Simple Food Webs as Energy Filters. II. Two-Species Systems, The American Naturalist 107, no.953953 (Oct 2015): 122–151.https://doi.org/10.1086/282820

Population modeling: a systems approach.

A single species population dynamics model based on the functional representations of birth, growth, and death has been constructed. Laboratory parameter estimates were used in a computer implementation of the model to simulate field populations. Preliminary results of replicate runs with parametric sampling indicated reasonable statistical agreement. Further development with the systems analysis technique is planned.

A model incorporating energy utilization for the dynamics of single species populations

A model for the population dynamics of a single species of animals is developed. The model consists of three ordinary differential equations expressing the rates of change of the state variables: density of animals, mean biomass per animal and food density; and several algebraic equations. The model differs from previous models in that mean biomass is used as an index of the size-age structure of the population, energy utilization by the population is considered, and a dimensionless form is developed. Terms are included for food supply rates and harvest rates. The results of computer simulations are presented and the properties of the model, including its stability and sensitivity to varying the parameters and initial conditions are discussed.

Applying Models Incorporating Age‐Size Structure of a Population to Daphnia

Partial differential equations which describe the dynamics of single species populations are applied to Daphnia pulex. Whenever possible, experimental results are used to determine pertinent parameters. Tests are performed to find parameters upon which the model has a critical dependence. The model gives results which are qualitatively in agreement with empirical populations.

A New Model For Age‐Size Structure of a Population

An equation describing the dynamics of single species populations is derived. The model allows for variations in the physiological characteristics of animals of different ages and sizes. An analytical solution which holds under certain specific conditions is found. It is shown that Von Foerster's equation, the logistic equation and other prior models are special cases of the new model.

THE FITNESS OF SINGLE-SPECIES POPULATIONS OF DROSOPHILA.

A population bottle technique for the maintenance of continuous populations of Drosophila (Barker, 1960) has been used in studies of interspecific competition and population fitness (Barker, 1963 a, b). In these studies, the wild type Oregon-R-C stock of D. melanogaster and the vermilion eye-color mutant of D. simulans have been used extensively, and when in competition, the latter is rapidly eliminated. In a current series of experiments, the nature of this interspecific competition is being studied, but the dynamics of single-species populations provide useful comparative information. With the description of the technique (Barker, 1960), some results for average population numbers of D. melanogaster and D. simulans over 11 generations were presented. These same populations have been maintained for 222 weeks (111 generations, Barker, 1962, 1967) and provide the data in this paper.